Introduction

Abstract

The restricted problem of three bodies has attracted the attention of many mathematicians and astronomers since it was first considered by Euler (1772) and Jacobi (1836). The most obvious reason for this continued interest is that the model of the restricted problem can serve as a first approximation in a number of real situations in astronomy (and more recently in astronautics). A deeper motivation comes probably from the fact that the general solution has not been found, in spite of the apparent simplicity of the problem. In fact, it seems now highly likely that such a general solution will never be found: numerical studies indicate that the restricted problem belongs to the general class of non-integrable dynamical systems with two degrees of freedom, and such systems are known to have an inexhaustible richness of detail in the behaviour of the solutions. In view of its simplicity, the restricted problem can then serve as a good model problem for the study of non-integrable systems.